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Chapter 0: Problem 10

Solve each linear equation. $$2(x-1)+3=x-3(x+1)$$

Short Answer

Expert verified
x = -1

Step by step solution

01

Distribute the Multiplication

Distribute the multiplication over the brackets. This gives \(2x - 2 + 3 = x - 3x - 3 \).
02

Simplify the Equation

Combine like terms on both sides of the equation. This simplifies the equation to \( 2x + 1 = -2x - 3 \).
03

Move Terms Involving x to One Side

Add \(2x\) to both sides of the equation to move all terms involving x to one side of the equation. This changes the equation to \(4x + 1 = -3\).
04

Isolate the Variable

Subtract 1 from both sides of the equation to isolate the variable x on the left side of the equation. This provides the solution \(x = -1\).

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Most popular questions from this chapter

Explain how to determine which numbers must be excluded from the domain of a rational expression.

Describe ways in which solving a linear inequality is different than solving a linear equation.

Use the strategy for solving word problems, modeling the verbal conditions of the problem with a linear inequality. A city commission has proposed two tax bills. The first bill requires that a homeowner pay \(\$ 1800\) plus \(3 \%\) of the assessed home value in taxes. The second bill requires taxes of \(\$ 200\) plus \(8 \%\) of the assessed home value. What price range of home assessment would make the first bill a better deal?

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